The invention relates to biodegradable polyester mixture, comprising i) from 5 to 80% by weight, based on the total weight of components i to ii, of at least one polyester based on aliphatic and aromatic dicarboxylic acids and on aliphatic dihydroxy compounds, and ii) from 20 to 95% by weight, based on the total weight of components i to ii, of at least one biodegradable homo- or copolyester selected from the group consisting of polylactide, polycaprolactone, polyhydroxyalkanoates, and polyesters composed of aliphatic dicarboxylic acids and of aliphatic diols, and iii) from 0.1 to 15% by weight, based on the total weight of components i to ii, a) of a copolymer containing epoxy groups and based on styrene, acrylate, and/or methacrylate, b) of a bisphenol A epoxide, or c) of a fatty acid amide or fatty acid ester or natural oil containing epoxy groups; and iv) from 0 to 15% by weight of additive; and v) from 0 to 50% by weight of inorganic or organic filler, and also to processes for their preparation and a method for their use.